TLDR: Schulman’s split is better stated as idea-driven versus goal-driven research. Idea-driven starts from the literature: follow a thread, find a gap or improvement, and test it. Goal-driven starts from a capability: pick a concrete problem you want to make work, then use the literature as tools for getting there.
Your framing is mostly right, but the correction is that goal-driven research should not mean only “a problem I personally like.” The goal needs to be specific, externally checkable, and broad enough that solving it teaches something general.